# -3dB passband on filters

I know with most op amp based filters and passive filters its common that the passband is -3dB which I understand as like for example if I would to make a bandpass filter, the beginning and end of the passband is -3dB attenuated while the center part of the filter is mostly the same dB unless you are making a Chebyshev filter.

So the question I am basically asking, was the -3dB passband common when filters where made with vacuum tubes? or was this introduced sometime when filters started to be made with op amps?

EDIT:

The only reason why I am confused about the -3dB passband of filters, is there are some filters calculators for example that you can change the attenuation of the passband, like if I wanted a -1dB instead of a -3dB passband for a bandpass filter A calculator that I have used can do that but it does default to -3dB.

There is another filter calculator that also ignores the passband attenuation and makes the entire frequency range the same gain instead of like a bandpass filter having -3dB at the ends of the passband, but this is only if you select Chebyshev type of filter.

• It flows out of some filter mathematics. So it dates way back -- long before ICs. (But it doesn't flow out of every kind of filter mathematics.)
– jonk
Commented Oct 18, 2021 at 5:34
• Minus 3 db is half the power, so that seems like a good measure of frequency response. Commented Oct 18, 2021 at 5:43
• Op amps were made with vacuum tubes before transistors existed. And filters do not need op-amps or vacuum tubes to exist as passive filters are common and they also have a half power point. Commented Oct 18, 2021 at 13:38

was the -3dB passband common when filters where made with vacuum tubes aka before op amps existed, or was this introduced sometime when filters started to be made with op amps?

Filters are fundamentally created by the interactions of resistors, capacitors and inductors. Active components can bring a bit more to the party but, fundamentally, it's the passive components that "make" the filter. The 3 dB point is equivalent to the power dropping by 50% on the filter output and this is true whether you use active devices or not.

For instance, a simple RC low pass filter produces a 3 dB drop in output signal level when the impedance of the capacitor in ohms equals the resistance of the resistor i.e.: -

$$R = \dfrac{1}{2\pi f C}$$

If you manipulate that formula you find that the "-3 dB" frequency: -

$$f = \dfrac{1}{2\pi R C}$$

The above has nothing to do with tubes, transistors or op-amps.

When - for a special application - I need a filter where the passband is characterized with "max damping of 1 dB for frequencies of interest", then I have the definition for the passband based on the "-1 dB criterion".

That means: The designer is free to define the passband within limits that are governed by the special application.

The same applies - as you know - for the stopband.

The only reason for a "common agreement" (3dB limits) is the wish to simplify the designers work - and tabulate some typical data (pole data or normalized parts values), based on passband edges which are given with the tables (3 dB for Butterworth and ripple values for Chebyshev).

But there is certainly no fixed "definition" for passband edges at -3dB points.

Using the -3dB point as the cutoff frequency applies to passive filters as well (those constructed with only resistors, inductors, and capacitors.) It really doesn't matter if it's an active filter (using an op-amp) or a passive filter with RLC components. The -3dB point applies in both cases.

Obviously tubes predate op-amps. There are tube designs, like the long tail pair, that function similar to an op-amp with inverting and non-inverting inputs. However, my understanding is that the idea of a global feedback loop (from the output back to the inverting input) came later. This may explain why many tube amplifier circuits use passive tone controls.

• Just FYI, R. P. Sallen and E. L Key wrote "TR-50: A Practical Method of Designing RC Active Filters," published on 6 May 1954. It refers only to vacuum tubes amplifier systems (no ICs or commercial BJTs back then.) Look up Harold Black on this Wiki page on NFB and see that global NFB goes back to somewhere into the 1920s/1930s. Quite early. Given that active elements were power-hungry vacuum tubes the desire to do more with passives was pretty strongly motivated.
– jonk
Commented Oct 18, 2021 at 5:28